Resonator having distributed transconductance elements

ABSTRACT

A method includes forming a resonator comprising a plurality of switched impedances spatially distributed within the resonator, selecting a resonant frequency for the resonator, and distributing two or more transconductance elements within the resonator based on the selected resonant frequency. Distributing the two or more transconductance elements may include non-uniformly distributing the two or more transconductance elements within the resonator.

STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH

This invention was made with Government support under Contract No.:HR0011-12-C-0087 awarded by the Defense Advanced Research ProjectsAgency (DARPA). The Government has certain rights in this invention.

FIELD OF THE INVENTION

The present application relates generally to resonators and, moreparticularly to control of resonant frequencies.

BACKGROUND

Resonators are used in various different circuits and integratedcircuits (chips). Resonators can have a plurality of different resonantfrequencies. Resonators include electrical circuits such as LC circuitswhich include an inductor and a capacitor. Some resonators include anarray of capacitors, or more generally impedances, which are tuned byselectively switching capacitors in the array. Resonators are used togenerate signals having a particular desired frequency. Filters may alsouse switched impedances to generate a desired narrowband passbandfunction.

SUMMARY

Embodiments of the invention provide techniques for improved control ofresonant frequencies in a resonator.

In one embodiment, an apparatus comprises a resonator. The resonatorcomprises a plurality of switched impedances spatially distributedwithin the resonator and a corresponding plurality of transconductanceelements distributed within respective distances among the switchedimpedances. The resonator has a given desired resonant frequency and agiven amplitude of response. Combined pairs of the switched impedancesand transconductance elements have respective parasitic resonantfrequencies which are higher than the given desired resonant frequencyand have respective amplitudes of response which are lower than thegiven amplitude of response.

In another embodiment, an integrated circuit comprises a resonator. Theresonator comprises a plurality of switched impedances spatiallydistributed within the resonator and a corresponding plurality oftransconductance elements distributed within respective distances amongthe switched impedances. The resonator has a given desired resonantfrequency and a given amplitude of response. Combined pairs of theswitched impedances and transconductance elements have respectiveparasitic resonant frequencies which are higher than the given desiredresonant frequency and have respective amplitudes of response which arelower than the given amplitude of response.

In another embodiment, a method comprises forming a resonator comprisinga plurality of switched impedances spatially distributed within theresonator and forming a plurality of transconductance elements withinrespective distances among the switched impedances. The resonator has agiven desired resonant frequency and a given amplitude of response.Combined pairs of the switched impedances and transconductance elementshave respective parasitic resonant frequencies which are higher than thegiven desired resonant frequency and have respective amplitudes ofresponse which are lower than the given amplitude of response.

Advantageously, embodiments of the invention distribute transconductancewithin a resonator to attain a desired dominant resonant mode and/ornarrowband bandpass response.

These and other features, objects and advantages of the presentinvention will become apparent from the following detailed descriptionof illustrative embodiments thereof, which is to be read in connectionwith the accompanying drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 shows a resonator including a distributed capacitor network,according to an embodiment of the invention.

FIG. 2 shows resonant modes of the resonator of FIG. 1, according to anembodiment of the invention.

FIG. 3 shows another resonator including a distributed capacitornetwork, according to an embodiment of the invention.

FIG. 4 is a chart illustrating resonant frequencies in a distributedimpedance network, according to an embodiment of the invention.

FIG. 5 is a chart illustrating resonant frequencies in a distributedimpedance network with lumped transconductance, according to anembodiment of the invention.

FIG. 6 is a chart illustrating resonant frequencies in a distributedimpedance network with distributed transconductance, according to anembodiment of the invention.

FIG. 7 shows an active filter, according to an embodiment of theinvention.

FIG. 8 shows another active filter, according to an embodiment of theinvention.

FIG. 9 shows another active filter, according to an embodiment of theinvention.

FIG. 10 is a chart illustrating frequency response for the active filterof FIG. 9, according to an embodiment of the invention.

FIG. 11 is a flow diagram showing a process for distributingtransconductance in an impedance array, according to an embodiment ofthe invention.

FIG. 12 is a block diagram of an integrated circuit including aresonator, according to an embodiment of the invention.

FIG. 13 is a block diagram of an integrated circuit including a filter,according to an embodiment of the invention.

DETAILED DESCRIPTION

Illustrative embodiments of the invention will be described herein inthe context of resonators used in circuits such as voltage controlledoscillators and active filters. However, it is to be understood thatprinciples of the invention are not limited solely to the specificarchitectures described herein. For example, the inventive techniquescan be used in a number of other types of circuits, oscillators,filters, etc. for improving selection of a desired resonant frequency orresponse.

In various types of circuits, including low frequency resonators andnarrowband filters, an assumption is made that capacitors, inductors andtransconductance in the circuits are lumped elements. This assumption,however, breaks down when considering a large array of switchedimpedances. An example of such an array is a large capacitor array usedin circuits such as voltage controlled oscillators (VCOs) and narrowbandbandpass active filters.

For example, VCOs for highly reconfigurable applications such assoftware defined radios, signal intelligence, spectrum scanning andsensing applications, etc. require a large tuning range, andconsequently large capacitor arrays. Hybrid architectures for such VCOsrequire a large number of individual varactors. In addition, a largetuning range may be required to counter process variation and provideversatility and programmability. In this case, a capacitor array isconsidered to be large if its physical dimension exceeds 1/100 of thewavelength of the signal of interest in the material. In someembodiments, a capacitor array is considered to be large when thephysical dimensions of a circuit including the array are greater than1/1000 of a wavelength of the circuit. In other embodiments, a capacitorarray is considered to be large when the physical dimensions of acircuit including the array are greater than 1/100 of a wavelength ofthe circuit. The particular application and design of a circuitincorporating an impedance array affects whether the array is consideredto be large such that the lumped assumption breaks down based on thephysical dimensions of the circuit and the wavelength of the signal ofinterest.

As another example, large capacitor arrays are required for filters usedin applications that include reconfigurable or wide tuning filters foranti-aliasing in variable rate ADCs. Large capacitor arrays are alsoused for reconfigurable filters in software defined radios, spectrumsensors, and signal intelligence applications. Scaled technologiesenable radio frequency (RF) signal processing using switched capacitors.RF processing prior to digitization for wide-band or high dynamic rateapplications requires high frequency transconductance-capacitance (Gm-C)filters. The RF processing front-end requires programmability. A largenumber of varactors are required for digital control and to counterprocess, temperature and voltage (PVT) variation in scaled processes.

Large capacitor arrays are distributed networks at RF and mm-wavefrequencies. For example, at high frequencies, interconnects betweencapacitors are inductive. For example, in a resonator with an operatingfrequency greater than 5 GHz, interconnects between capacitors, and moregenerally impedances, are inductive. The particular operating frequencymay vary based on the particular application and design of a circuitincorporating the impedance array. For example, in some embodiments aresonator may have an operating frequency greater than 20 GHz.

A resonator with a high quality (Q) factor can be used to reduce theinductance in such interconnects. High Q capacitors, however, are areainefficient.

Conventional techniques assume lumped transconductance in a lumpedswitched capacitor array. Large switched capacitor arrays, however, aredistributed resonant (LC) networks where multiple resonances arepossible. Of the multiple resonances, there is a desired or preferredresonance and one or more parasitic resonances. Such parasiticresonances may result from parasitic inductances of interconnects in acapacitor array. Embodiments of the invention utilize distributedtransconductance elements or cells to enable large switched capacitorarrays in which the parasitic resonances are reduced or minimized. Usingdistributed transconductance elements, the preferred resonance will seea large transconductance while parasitic modes see a lowertransconductance.

For example, in some embodiments a distributed active resonatorincluding multiple capacitors and inductors (which may or may not beequal) has a required transconductance which is distributed acrossmultiple nodes in the resonator in a way that a single dominant resonantmode is attained. The transconductance may be non-uniformly distributedacross nodes in the resonator. Resonators may be implemented in varioustypes of VCOs, including by way of example wide-tuning rangeoscillators, digitally controlled oscillators, millimeter waveoscillators, and combinations of such VCOs.

As another example, in some embodiments a distributed active filterincluding multiple capacitors and inductors (which may or may not beequal) has a required transconductance which is distributed acrossmultiple nodes in a way that a single dominant narrowband bandpassresponse is attained. Again, the transconductance may be non-uniformlydistributed in the active filter. Active filters may be one of a varietyof types of filters, including by way of example switched impedancefilters, switched capacitor transconductance filters, programmablenarrowband band select filters, and combinations of such filters.Various other types of circuits may utilize distributedtransconductance, including combinations of the resonators and filters.

Embodiments of the invention will be described below primarily in thecontext of switched capacitor arrays. Embodiments, however, are notlimited solely to use with switched capacitor arrays. Instead,embodiments may more generally use switched impedance arrays.

FIG. 1 shows a distributed capacitor network for a resonator 100. Theresonator 100 circuit is an LC circuit, including an inductor L andgroups of switched capacitors C. Switches SW₁, SW₂ and SW₃ are used toswitch in the respective groups of capacitors C. Various types ofswitches may be used, including transistors and logic gates. Largetuning range LC resonators, such as resonator 100, use large capacitorarrays. The interconnects between the capacitors C in resonator 100contribute parasitic inductances, labelled as L_(p) in FIG. 1. Theresonator includes positive and negative outputs OUT+ and OUT−. Theoutput of the resonator varies based on which of the capacitors areswitched in using switches SW₁, SW₂ and SW₃.

The resonator 100 is a distributed LC network where multiple resonancesare possible (e.g., a higher order network). The resonator 100 includesdistributed transconductance elements, such as G_(m) cells 102, 104 and106 to achieve a desired dominant resonant frequency. The G_(m) cells102, 104 and 106 are distributed within the resonator such that only thedesired resonant mode sees the entire transconductance. Parasitic modes,as will be discussed in further detail below, see only a fraction of thetotal transconductance.

FIG. 2 shows the parasitic modes of the resonator 100. Because of thedistributed G_(m) cells 102, 104 and 106, local loops within theresonator see only a fraction of the total transconductance. The localresonant modes RM₁, RM₂, RM₃, RM₄ and RM₅ have a small gain. If thetransconductance were not distributed within the resonator 100, theparasitic inductances would cause much higher parasitic resonant modes.In some instances, such parasitic modes would dominate the responseinstead of the desired resonant mode. For example, a capacitor at lowfrequency may be a short at high frequency. In circuits such as VCOs,this leads to parasitic oscillations at high frequencies. In circuitssuch as filters, multiple bandpass peaks degrade filtering performanceby causing poor selectivity.

In some embodiments, as discussed above, the transconductance may benon-uniformly distributed within a resonator. FIG. 3 shows a distributedcapacitor network for a resonator 300. The resonator 300 is an LCcircuit, including an inductor L and groups of switched capacitorsC_(A), C_(B) and C_(C). Switches SW_(A), SW_(B) and SW_(C) are used toswitch in the respective capacitances C_(A), C_(B) and C_(C). The outputof the resonator 300 varies based on which of the capacitors areswitched in using the switches SW_(A), SW_(B) and SW_(C).

As illustrated visually in FIG. 3, capacitors C_(C) are larger thancapacitors C_(B), which are in turn larger than capacitors C_(A). Inother words, the capacitors in the resonator 300 are unequally sized.The magnitude of the capacitance associated with capacitors C_(C) isgreater than that of capacitors C_(B), which is in turn greater thanthat of capacitors C_(A).

Due to the varying capacitances of capacitors C_(A), C_(B) and C_(C),the parasitic inductances L_(P1), L_(P2), L_(P3), L_(P4) and L_(P5)caused by interconnects between the capacitors in the resonator 300 arealso unequal. To reduce the parasitic inductances in the resonator 300,the transconductance is non-uniformly distributed via the G_(m) cells302, 304 and 306. FIG. 3 visually illustrates the non-uniformdistributed of transconductance in the varying sizes of the G_(m) cells302, 304 and 306. The largest G_(m) cell 306 is distributed within afirst distance of the largest capacitors C_(C). The next largest G_(m)cell 304 is distributed within a second distance of the next largestcapacitors C_(B), and the smallest G_(m) cell 302 is distributed withina third distance of the smallest capacitors C_(A).

The first, second and third distances are based on the respective sizesof the capacitances and transconductance elements. In some embodiments,the first, second and third distances are minimized. For example, thelargest transconductance is placed as close as possible to the largestcapacitor, the second largest transconductance is placed as close aspossible to the second largest transconductance, etc. The resultingG_(m)-C blocks are then placed as close to one another as possible.

The respective distances between switched impedances such as capacitorsC_(A), C_(B) and C_(C) and transconductance elements such as G_(m) cells302, 304 and 306 may be controlled based on the relationship between theimpedance values and the transconductance values. For example, thetransconductance in resonator 300 is distributed among the unequalcapacitors C_(A), C_(B) and C_(C). The magnitudes of G_(m) cells 302,304 and 306 are denoted G_(m,A), G_(m,B) and G_(m,C), respectively. Thetransconductance is proportionally distributed based on the magnitudesof the capacitances C_(A), C_(B) and C_(C), e.g., G_(m,A)αC_(A);G_(m,B)αC_(B); and G_(m,C)αC_(C). The resonator 300 thus hasnon-uniformly distributed transconductance such that the resonantfrequencies of the parasitic interconnect inductances increases whiletheir respective amplitudes of response decrease.

It is important to note that while FIG. 3 visually shows C_(C) and G_(m)cell 306 as twice the size of C_(B) and G_(m) cell 304 and visuallyshows C_(B) and G_(m) cell 304 as twice the size of C_(A) and G_(m) cell302, respectively, embodiments are not limited solely to thisarrangement. Capacitor arrays in embodiments of the invention may haveunequally sizes capacitors which do not necessarily increase in size bya factor of two. Instead, capacitor arrays can have unequally sizedcapacitors in which their sizes increase or decrease by a factor greaterthan or less than two. In addition, while FIGS. 1-3 show capacitorarrays in resonators having three groups of switched capacitors,embodiments are not limited solely to capacitor arrays having threegroups of switched capacitors. Instead, embodiments include capacitorarrays having two groups of switched capacitors and greater than threegroups of switched capacitors.

FIGS. 4-6 are charts which illustrate resonant frequencies in adistributed impedance network. FIG. 4 shows the magnitude of theimpedance |Z| as a function of increasing frequency. The switchedimpedance network in FIG. 4 may comprise a resonator such as resonator100 or resonator 300. Interconnects in the impedance array contributeparasitic inductance which in turn lead to parasitic frequency modes asillustrated in FIG. 4.

FIG. 5 shows the transconductance multiplied by the magnitude of theimpedance, g_(m)|Z| for a lumped transconductance element in theswitched impedance array plot of FIG. 4. As shown in FIG. 5, theparasitic modes dominates the desired mode.

FIG. 6 shows the g_(m)|Z| using distributed transconductance as afunction of increasing frequency in the switched impedance array plot ofFIG. 4. As shown, the desired mode dominates, as the parasitic modes areweaker (e.g., lower amplitude) and at higher frequencies. At the higherfrequencies, transconductance or G_(m) is much lower, such that thelocal loops formed by distributed transconductance elements see only afraction of the total transconductance. FIG. 2, which is discussedabove, illustrates an example of such local loops for resonator 100.Distributing the transconductance increases the number of parasiticmodes, but the parasitic modes are pushed to higher frequencies. Inother words, the parasitic modes have lower amplitudes of response andhigher frequencies than the desired mode.

FIG. 7 shows an active filter 700 having distributed transconductance.The filter has an input IN which is input to transconductance elements702, 704 and 706. The transconductance elements are connected torespective capacitors C. Each capacitor C is connected between atransconductance element and ground or a voltage return of the filter700. The transconductance elements 704 and 706 are switchably coupled totheir respective capacitors C via switches SW₁ and SW₂. By distributingthe transconductance, rather than using a lumped transconductanceelement coupled to all of the capacitors C, the active filter provides aparasitic ripple-free response.

FIG. 8 shows an active filter 800 having non-uniformly distributedtransconductance. The filter 800 has an input IN coupled totransconductance elements 802, 804 and 806. Capacitors C_(A), C_(B) andC_(C) are coupled between the respective transconductance elements 802,804 and 806 and ground or a voltage return of the filter 800. Similar tothe resonator 300 discussed above, the transconductance elements 802,804 and 806 are distributed proportionally based on the magnitudes ofthe capacitances C_(A), C_(B) and C_(C). Transconductance element 802has transconductance G_(m,A), transconductance element 804 hastransconductance G_(m,B) and transconductance element 806 hastransconductance G_(m,C), where G_(m,A)αC_(A), G_(m,B) αC_(B), andG_(m,C)αC_(C). The active filter 800 thus has weighted distributedtransconductance.

While C_(A), C_(B) and C_(C) are visually represented in FIG. 8 asdoubling in size (e.g., C_(C) is 2C_(B) and C_(B) is 2C_(A)),embodiments are not limited solely to this specific distribution.Instead, the sizes of the capacitors in an active filter may vary insize by different factors (e.g., greater than or less than two). Inaddition, filters in other embodiments can have more than two or only asingle switchable capacitor.

FIG. 9 shows an active filter 900 with distributed transconductance. Thefilter 900 has an input IN and an output OUT. The filter 900 has anumber of desired impedances 902. As shown, impedances 902-2 through902-M may be selectively switched in. Interconnects between theimpedances 902, however, produce parasitic impedances 904. The parasiticimpedances 904 cause undesired zeroes which reduce frequency selectivityin the filter 900. The filter 900 includes transconductance elements 906to suppress the parasitic impedances 904. The transconductance elements906 may be non-uniformly distributed within the filter 900 based on therespective sizes of the impedances 902 and 904 in a manner similar tothat described above with respect to filter 800.

FIG. 10 is a chart illustrating g_(m)|Z| for the filter 900 as afunction of frequency. As shown, the filter 900 achieves a desirednarrowband response because the transconductance is distributed tosuppress the parasitic modes caused by parasitic impedances 904. In someembodiments, transconductance elements are distributed within a filterbased on a target narrowband bandpass transfer function.

FIG. 11 shows a process 1100 for distributing transconductance in animpedance array. The process 1100 begins with step 1102 where, given animpedance array and a total transconductance, the total transconductanceis divided into one or more partial transconductances for respectiveassociated switched impedances in the array. In step 1104, the partialtransconductances are weighted based on the magnitudes of the associatedswitched impedances. For example, as described above with respect toFIGS. 3 and 8, the transconductance elements are weighted in proportionto the respective switched capacitances.

The partial transconductances are then placed within the impedance arrayat respective distances from the associated switched impedances in step1106. Next, a determination is made in step 1108 as to whether anyparasitic modes are present. If parasitic modes are present, the process1100 continues to step 1110. Otherwise, the process 1100 is finished instep 1112.

In step 1110, the partial transconductances are redistributed for givenones of the switched impedances which are causing the parasitic modes inthe impedance array. The partial transconductances are redistributed bymoving the partial transconductances associated with the given switchedimpedances close to the given switched impedances. The process 1100 thenreturns to step 1108 to determine if the parasitic modes are stillpresent. In other embodiments, in addition to or in place of moving thepartial transconductances closer to the given switched impedances, therespective weightings of the transconductances may be adjusted.

Embodiments may be implemented in integrated circuits. For example, FIG.12 shows an integrated circuit 1200 including a resonator 1210. Theresonator 1210 may be the resonator 100, the resonator 300, or anotherresonator with distributed transconductance in accordance withembodiments of the invention. FIG. 13 shows an integrated circuit 1300including a filter 1310. The filter 1310 may be one of the filters 700,800 or 900, or another filter with distributed transconductance inaccordance with embodiments of the invention.

It is to be appreciated that, in an illustrative integrated circuitimplementation of the invention, such as that shown in FIG. 12 or FIG.13, one or more integrated circuit dies are typically formed in apattern on a surface of a wafer. Each such die may include a devicecomprising circuitry as described herein, and may include otherstructures or circuits. The dies are cut or diced from the wafer, thenpackaged as integrated circuits. One ordinarily skilled in the art wouldknow how to dice wafers and package dies to produce packaged integratedcircuits. Integrated circuits, manufactured as above and/or in otherways, are considered part of this invention. While the resonator 1210and filter 1310 are shown in FIGS. 12 and 13, respectively, as beingformed in one integrated circuit, it is to be understood that thecircuits can be formed across multiple integrated circuits.

It will be appreciated and should be understood that the exemplaryembodiments of the invention described above can be implemented in anumber of different fashions. Given the teachings of the inventionprovided herein, one of ordinary skill in the related art will be ableto contemplate other implementations of the invention. Indeed, althoughillustrative embodiments of the present invention have been describedherein with reference to the accompanying drawings, it is to beunderstood that the invention is not limited to those preciseembodiments, and that various other changes and modifications may bemade by one skilled in the art without departing from the scope orspirit of the invention.

What is claimed is:
 1. An apparatus comprising: a resonator comprising:a plurality of switched impedances spatially distributed within theresonator; and a corresponding plurality of transconductance elementsdistributed within respective distances among the switched impedances;wherein the resonator has a given desired resonant frequency and a givenamplitude of response; and wherein combined pairs of the switchedimpedances and transconductance elements have respective parasiticresonant frequencies which are higher than the given desired resonantfrequency and have respective amplitudes of response which are lowerthan the given amplitude of response.
 2. The apparatus of claim 1wherein the apparatus is a voltage controlled oscillator.
 3. Theapparatus of claim 2 wherein the voltage controlled oscillator comprisesat least one of a wide-tuning range oscillator, a digitally controlledoscillator and a millimeter wave oscillator.
 4. The apparatus of claim 1wherein the apparatus is an active filter.
 5. The apparatus of claim 4wherein the active filter comprises at least one of a switched impedancefilter, a switched capacitor transconductance filter and a programmablenarrowband band select filter.
 6. The apparatus of claim 1 wherein theswitched impedances comprise a capacitor array.
 7. The apparatus ofclaim 6 wherein: one or more interconnects between capacitors in thecapacitor array contribute respective parasitic inductances in theresonator; and the transconductance elements are distributed within thecapacitor array to reduce the parasitic inductances of the one or moreinterconnects.
 8. The apparatus of claim 1 wherein: the transconductanceelements have associated therewith different transconductance values;the switched impedances comprise capacitors having associated therewithdifferent capacitance values; and wherein the transconductance elementsare distributed within the resonator such that the transconductancevalues are proportional to the capacitance values.
 9. The apparatus ofclaim 8 wherein a given distance between a given switched impedance anda given transconductance element is controlled based on a relationshipbetween the capacitance value of the given switched impedance and thetransconductance value of the given transconductance element.
 10. Theapparatus of claim 1 wherein: the transconductance elements haveassociated therewith different transconductance values; the switchedimpedances comprise inductors having associated therewith differentinductance values; and wherein the transconductance elements aredistributed within the resonator such that the transconductance valuesare proportional to the inductance values.
 11. The apparatus of claim 10wherein a given distance between a given switched impedance and a giventransconductance element is controlled based on a relationship betweenthe inductance value of the given switched impedance and thetransconductance value of the given transconductance element.
 12. Theapparatus of claim 1 wherein the transconductance elements aredistributed based on a target narrowband bandpass transfer function. 13.The apparatus of claim 1 wherein an operating frequency of the resonatoris 20 gigahertz or greater.
 14. The apparatus of claim 1 whereinphysical dimensions of the apparatus are greater than 1/100 of awavelength of the apparatus.
 15. The apparatus of claim 1 whereinphysical dimensions of the apparatus are greater than 1/1000 of awavelength of the apparatus.
 16. An integrated circuit comprising: aresonator comprising: a plurality of switched impedances spatiallydistributed within the resonator; and a corresponding plurality oftransconductance elements distributed within respective distances amongthe switched impedances; wherein the resonator has a given desiredresonant frequency and a given amplitude of response; and whereincombined pairs of the switched impedances and transconductance elementshave respective parasitic resonant frequencies which are higher than thegiven desired resonant frequency and have respective amplitudes ofresponse which are lower than the given amplitude of response.
 17. Avoltage controlled oscillator comprising the integrated circuit of claim16.
 18. An active filter comprising the integrated circuit of claim 16.19. A method comprising: forming a resonator comprising a plurality ofswitched impedances spatially distributed within the resonator; andforming a plurality of transconductance elements within respectivedistances among the switched impedances; wherein the resonator has agiven desired resonant frequency and a given amplitude of response; andwherein combined pairs of the switched impedances and transconductanceelements have respective parasitic resonant frequencies which are higherthan the given desired resonant frequency and have respective amplitudesof response which are lower than the given amplitude of response.